Department of Mathematics

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Author: search.filters.author.Kulshrestha, RakheeEnd date: 2009

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    Reliability Analysis of Redundant Repairable System with Degraded Failure
    (MERC, 2004) Kulshrestha, Rakhee
    This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation there is a facility of one additional repairman to speed up the repair. The lifetime and repair time of units are exponentially distributed. We use matrix method to solve the governing Chapman-Kolmogorov equations. Expressions for the system reliability, availability, mean time to system failure, etc. are established in terms of transient probability. Computational scheme is discussed to facilitate the numerical results. Sensitivity analysis is also carried out to depict the effect of various parameters on the system reliability.
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    Bilevel control of degraded machining system with warm standbys, setup and vacation
    (Elsevier, 2004-12) Kulshrestha, Rakhee
    In this paper, we study (N, L) switch-over policy for machine repair model with warm standbys and two repairmen. The repairman (R1) turns on for repair only when N-failed units are accumulated and starts repair after a set up time which is assumed to be exponentially distributed. As soon as the system becomes empty, the repairman (R1) leaves for a vacation and returns back when he finds the number of failed units in the system greater than or equal to a threshold value N. Second repairman (R2) turns on when there are L(>N) failed units in the system and goes for a vacation if there are less than L failed units. The life time and repair time of failed units are assumed to be exponentially distributed. The steady state queue size distribution is obtained by using recursive method. Expressions for the average number of failed units in the queue and the average waiting time are established.
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    N-policy for a machine repair system with spares and reneging
    (Elsevier, 2004-06) Kulshrestha, Rakhee
    This paper deals with the reliability characteristics of a machine repairable system with M-operating and S warm standby units. The units are assumed to fail in Poisson fashion. There is a provision of a removable repairman which repairs failed units according to exponential distribution. Due to impatience, the failed units may renege when repairman is busy. When N or more units are failed, the removable repairman turns on and starts the repair work. The repairman turns off when the system is empty. We use Laplace transforms technique to derive the explicit expressions of the reliability function and the mean time to system failure. Numerical results to highlight the effects of various system parameters to the reliability indices on the system have been provided.
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    A subrating channel assignment scheme for cellular radio network with directed retry
    (Elsevier, 2005-09) Kulshrestha, Rakhee
    In this paper the subrating channel assignment scheme is used to improve the performance of handoff packets. The subrating of a channel is done by dividing temporarily a full-rate channel into two half rate channels. Hand-off voice calls may also be served by subrated channels if all channels of the BS are occupied. The subrating of channels can degrade the quality, but it improves the grade of service (GOS) for hand-off calls and minimizes the delay. The provision of directed retry in overlapping area among neighbouring cells is also done for handoff attempts so that the blocking of handoff traffic can be checked to some extent. By using an iterative algorithm we obtain performance indices such as blocking probabilities, degradation in quality, total carried load, dwell time, etc. Numerical results have also been facilitated to prove the validity of the proposed iterative algorithm.
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    Transient Analysis of a Telecommunication System Using State Dependent Markovian Queue under Bi-Level Control Policy
    (JKAU, 2009) Kulshrestha, Rakhee
    In this paper, we develop a finite queueing model having single and batch service modes for telecommunication system, where two types of traffic, i.e. voice and data arrive in Poisson fashion. The server starts service only when N packets are accumulated in the system. The server performs service singly until there are C packets in the system. After then type 2 packets are discarded and all type 1 packets are served in a batch. The arrival rates of packets depend upon the server’s status. The transient state probabilities of system states are obtained by solving a set of linear equations with the help of Laplace Transform technique. Performance indices such as average queue length, expected idle time, and expected busy period are determined. We also investigate the optimal value of threshold parameter N and C after which the server changes the mode of service in order to minimize the expected cost. The numerical illustrations are provided to visualize the effect of various parameters on system performance